Finite Group Databasebeta

← #14326882

Subgroups — #14326882

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#892C211yesmaximal, characteristic
2#11752371C211yesmaximal, characteristic, complemented
3C3×#65712C211yesmaximal, characteristic, complemented
4#11751855C211yesmaximal, characteristic
5C4×(C2×D3)⋊AGL(1,𝔽5)C211yesmaximal, characteristic
6#11751846C211yesmaximal, characteristic, complemented
7#11751841C212yesmaximal
8AGL(1,𝔽5)×C4⋊Dic3C211yesmaximal, characteristic, complemented
9#11751836C212yesmaximal
10#11751832C212yesmaximal, complemented
11#11751751C212yesmaximal, complemented
12#10617133—31nomaximal, Hall
13C2×C4×D3×D5C2211yescharacteristic
14C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
15C2×C4⋊ΓL(1,𝔽16)C2212yes—
16C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
17C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
18C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
19C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
20C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
21C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
22C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
23C2×Dic3×AGL(1,𝔽5)C2212yes—
24C2×Dic3×AGL(1,𝔽5)C2212yes—
25#91781C411yescharacteristic, complemented
26C5×#892C411yescharacteristic, complemented
27C3×D5×C4⋊C4C2211yescharacteristic
28D5×(C2×D3)⋊C4C2212yes—
29D5×C4⋊Dic3C2211yescharacteristic
30#91403C412yescomplemented
31#91400C412yescomplemented
32C4×D5×Dic3C2212yes—
33#91347C411yescharacteristic, complemented
34#91338C411yescharacteristic, complemented
35#91235C2212yes—
36C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
37(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
38(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
39(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
42#75979—51nomaximal, Hall
43D5×#117—31no—
44#65765—31no—
45C4×C22⋊AGL(1,𝔽5)—31no—
46#65712—31no—
47#65712D311yescharacteristic, complemented
48C4⋊C4×AGL(1,𝔽5)—31no—
49C4⋊C4×AGL(1,𝔽5)—31no—
50#65700—32no—
51#65700—32no—
52#65689—32no—
53#65686—32no—
54C22×D3×D5C2311yescharacteristic
55C22×ΓL(1,𝔽16)C2312yes—
56C22×ΓL(1,𝔽16)C2311yescharacteristic
57C22×ΓL(1,𝔽16)C2311yescharacteristic
58C22×C3×AGL(1,𝔽5)C2312yes—
59C22×C3×AGL(1,𝔽5)C2311yescharacteristic
60C22×C3×AGL(1,𝔽5)C2311yescharacteristic
61C2×C4×D15C2×C411yescharacteristic
62C2×C4×C5×D3C2×C411yescharacteristic
63C2×C3×C4×D5C2312yes—
64C2×C3×C4×D5C2311yescharacteristic
65C2×#1200C2×C411yescharacteristic
66C2×D3×Dic5C2×C411yescharacteristic
67C2×D5×Dic3C2312yes—
68C2×D5×Dic3C2311yescharacteristic
69C4×D3×D5—22no—
70C4×D3×D5—22no—
71C4⋊ΓL(1,𝔽16)—22no—
72C4⋊ΓL(1,𝔽16)—42no—
73C4×ΓL(1,𝔽16)—22no—
74C3×C4⋊AGL(1,𝔽5)—22no—
75C3×C4⋊AGL(1,𝔽5)—42no—
76C3×C4×AGL(1,𝔽5)—22no—
77(C2×D3)⋊AGL(1,𝔽5)—22no—
78(C2×D3)⋊AGL(1,𝔽5)—22no—
79(C2×D3)⋊AGL(1,𝔽5)—42no—
80Dic3×AGL(1,𝔽5)—24no—
81Dic3×AGL(1,𝔽5)—24no—
82C3×C5×C4⋊C4C2×C411yescharacteristic
83#6714C2×C412yes—
84C4⋊Dic15C2×C411yescharacteristic
85C4×Dic15C2×C412yes—
86C5×(C2×D3)⋊C4C2×C412yes—
87C5×C4⋊Dic3C2×C411yescharacteristic
88C4×C5×Dic3C2×C412yes—
89C3×C4⋊Dic5C2×C411yescharacteristic
90C3×#683C2×C412yes—
91#6668C2×C412yes—
92#6667C2×C412yes—
93(C2×D3)⋊Dic5C2×C412yes—
94Dic3×Dic5C2×C412yes—
95Dic3×Dic5C2×C412yes—
96C2×#892—51no—
97C3×#389—51no—
98#4990—52no—
99#4987—51no—
100#4984—51no—
101#4977—52no—
102Dic3×C4⋊C4—51no—
103C4×(C2×D3)⋊C4—51no—
104C4×C4⋊Dic3—51no—
105#4670—52no—
106#4648—52no—
107C22×C4×D5—31no—
108C2×C22⋊AGL(1,𝔽5)—31no—
109C2×C22⋊AGL(1,𝔽5)—31no—
110C2×C22⋊AGL(1,𝔽5)—32no—
111C2×C4⋊AGL(1,𝔽5)—31no—
112C2×C4⋊AGL(1,𝔽5)—32no—
113C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
114C2×C4⋊AGL(1,𝔽5)C2×D312yes—
115C2×C4×AGL(1,𝔽5)—32no—
116C2×C4×AGL(1,𝔽5)—32no—
117C2×C4×AGL(1,𝔽5)—31no—
118C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
119C5×#117—31no—
120#4072—31no—
121#4038—31no—
122#4038—31no—
123D5×C4⋊C4—31no—
124D5×C4⋊C4C2×D311yescharacteristic
125D5×C22⋊C4—32no—
126#4023—32no—
127#4018—32no—
128C42×D5—32no—
129(C2×AGL(1,𝔽5))⋊C4—31no—
130(C2×AGL(1,𝔽5))⋊C4—32no—
131(C2×AGL(1,𝔽5))⋊C4—31no—
132(C2×AGL(1,𝔽5))⋊C4—32no—
133(C2×AGL(1,𝔽5))⋊C4—32no—
134(C2×AGL(1,𝔽5))⋊C4—32no—
135(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
136#2346—151noSylow
137C22×D15C22×C411yescharacteristic
138C22×C5×D3C22×C411yescharacteristic
139C22×C3×D5C2411yescharacteristic
140C2×D3×D5—21no—
141C2×D3×D5—21no—
142C2×D3×D5—21no—
143C2×D3×D5—21no—
144C2×D3×D5—21no—
145C2×D3×D5—21no—
146C2×ΓL(1,𝔽16)—21no—
147C2×ΓL(1,𝔽16)—21no—
148C2×ΓL(1,𝔽16)—22no—
149C2×ΓL(1,𝔽16)—21no—
150C2×ΓL(1,𝔽16)—21no—
151C2×ΓL(1,𝔽16)—22no—
152C2×ΓL(1,𝔽16)—22no—
153C2×ΓL(1,𝔽16)—21no—
154C2×ΓL(1,𝔽16)#4112yes—
155C2×C3×AGL(1,𝔽5)—21no—
156C2×C3×AGL(1,𝔽5)—21no—
157C2×C3×AGL(1,𝔽5)—22no—
158C2×C3×AGL(1,𝔽5)—21no—
159C2×C3×AGL(1,𝔽5)—21no—
160C2×C3×AGL(1,𝔽5)—22no—
161C2×C3×AGL(1,𝔽5)—22no—
162C2×C3×AGL(1,𝔽5)—21no—
163C2×C3×AGL(1,𝔽5)#4112yes—
164C2×C3×C4×C5C22×C412yes—
165C2×C3×C4×C5C22×C411yescharacteristic
166C2×Dic15C22×C411yescharacteristic
167C2×Dic15C22×C412yes—
168C4×D15—22no—
169C2×C5×Dic3C22×C411yescharacteristic
170C2×C5×Dic3C22×C412yes—
171C4×C5×D3—22no—
172C2×C3×Dic5C22×C412yes—
173C2×C3×Dic5C22×C411yescharacteristic
174C3×C4×D5—22no—
175C3×C4×D5—22no—
176C3×C4×D5#4112yes—
177C3×C4×D5#4112yes—
178#1200—22no—
179D3×Dic5—22no—
180D5×Dic3—22no—
181D5×Dic3—22no—
182D5×Dic3—21no—
183D5×Dic3—21no—
184C22×C4×D3—51no—
185C2×C3×C4⋊C4—51no—
186C2×C3×C4⋊C4—51no—
187C2×C3×C4⋊C4—52no—
188C2×C3×C42—51no—
189C2×(C2×D3)⋊C4—52no—
190C2×(C2×D3)⋊C4—51no—
191C2×(C2×D3)⋊C4—51no—
192C2×(C2×D3)⋊C4—52no—
193C2×C4⋊Dic3—51no—
194C2×C4⋊Dic3—51no—
195C2×C4⋊Dic3—52no—
196C2×C4×Dic3—52no—
197C2×C4×Dic3—52no—
198C2×C4×Dic3—52no—
199C2×C4×Dic3—51no—
200#892—51no—
201#892—51no—
202#892—52no—
203#892—51no—
204#892—52no—
205#892AGL(1,𝔽5)11yescharacteristic, complemented
206C3×#95—52no—
207C3⋊#95—51no—
208C3⋊#95—52no—
209C3⋊#95—52no—
210C3⋊#95—52no—
211C3⋊#95—51no—
212C3⋊#95—52no—
213C23×D5—31no—
214C22×AGL(1,𝔽5)—31no—
215C22×AGL(1,𝔽5)—31no—
216C22×AGL(1,𝔽5)—32no—
217C22×AGL(1,𝔽5)C22×D312yes—
218C22×AGL(1,𝔽5)C22×D311yescharacteristic
219C22×AGL(1,𝔽5)C22×D311yescharacteristic
220C22×C4×C5—31no—
221C22×Dic5—31no—
222C2×C4×D5—32no—
223C2×C4×D5—31no—
224C2×C4×D5—31no—
225C2×C4×D5—31no—
226C2×C4×D5—62no—
227C2×C4×D5—62no—
228C2×C4×D5C22×D312yes—
229C2×C4×D5C22×D311yescharacteristic
230C22⋊AGL(1,𝔽5)—62no—
231C22⋊AGL(1,𝔽5)—62no—
232C22⋊AGL(1,𝔽5)—122no—
233C4⋊AGL(1,𝔽5)—22no—
234C4⋊AGL(1,𝔽5)—42no—
235C4⋊AGL(1,𝔽5)—62no—
236C4⋊AGL(1,𝔽5)—122no—
237C4×AGL(1,𝔽5)—22no—
238C4×AGL(1,𝔽5)—64no—
239C4×AGL(1,𝔽5)—64no—
240C4×AGL(1,𝔽5)—62no—
241C5×C4⋊C4—31no—
242C5×C4⋊C4C4×D311yescharacteristic
243C5×C22⋊C4—32no—
244C42×C5—32no—
245C22⋊Dic5—32no—
246#685—32no—
247#685—32no—
248C4⋊Dic5—31no—
249C4⋊Dic5C4×D311yescharacteristic
250#683—32no—
251#683C4×D312yes—
252C4×Dic5—32no—
253C4×Dic5—32no—
254C4×Dic5—32no—
255C2×#117—151no—
256#389—51no—
257#389—151no—
258#388—152no—
259#388—152no—
260#382—152no—
261#380—151no—
262C4×C4⋊C4—151no—
263C4×C4⋊C4—151no—
264C4×C22⋊C4—151no—
265#376—152no—
266C22×C3×C5C23×C411yescharacteristic
267C2×D15—21no—
268C2×D15—21no—
269C2×D15—21no—
270C2×C5×D3—21no—
271C2×C5×D3—21no—
272C2×C5×D3—21no—
273C2×C3×D5C2×#4111yescharacteristic
274C2×C3×D5C2×#4111yescharacteristic
275C2×C3×D5C2×#4111yescharacteristic
276C2×C3×D5C2×#4111yescharacteristic
277C2×C3×D5H(5,𝔽2)11yescharacteristic
278C2×C3×D52−1+411yescharacteristic
279D3×D5—41no—
280D3×D5—41no—
281D3×D5—41no—
282D3×D5—41no—
283ΓL(1,𝔽16)—22no—
284ΓL(1,𝔽16)—42no—
285ΓL(1,𝔽16)—41no—
286C3×AGL(1,𝔽5)—22no—
287C3×AGL(1,𝔽5)—42no—
288C3×AGL(1,𝔽5)—41no—
289C3×C4×C5—22no—
290C3×C4×C5#11712yes—
291Dic15—21no—
292Dic15—22no—
293C3×Dic5—22no—
294C3×Dic5#11712yes—
295C5×Dic3—21no—
296C5×Dic3—22no—
297C23×D3—51no—
298C22×C3×C4—51no—
299C22×C3×C4—51no—
300C22×C3×C4—52no—
301C22×C3×C4—51no—
302C22×C3×C4—52no—
303C22×Dic3—51no—
304C22×Dic3—51no—
305C22×Dic3—52no—
306C22×Dic3—52no—
307C22×Dic3—51no—
308C2×C4×D3—51no—
309C2×C4×D3—51no—
310C2×C4×D3—51no—
311C2×C4×D3—102no—
312C2×C4×D3—102no—
313C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
314C3×C4⋊C4—52no—
315C3×C4⋊C4—51no—
316C3×C4⋊C4—102no—
317C3×C4⋊C4—202no—
318C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
319C3×C42—102no—
320(C2×D3)⋊C4—52no—
321(C2×D3)⋊C4—52no—
322(C2×D3)⋊C4—52no—
323(C2×D3)⋊C4—102no—
324(C2×D3)⋊C4—102no—
325(C2×D3)⋊C4—202no—
326(C2×D3)⋊C4C2×AGL(1,𝔽5)12yes—
327C4⋊Dic3—51no—
328C4⋊Dic3—52no—
329C4⋊Dic3—102no—
330C4⋊Dic3—202no—
331C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
332C4×Dic3—52no—
333C4×Dic3—52no—
334C4×Dic3—52no—
335C4×Dic3—104no—
336C4×Dic3—104no—
337C4×Dic3—102no—
338C4×Dic3C2×AGL(1,𝔽5)12yes—
339C23×C5—31no—
340C22×D5—31no—
341C22×D5—61no—
342C22×D5—61no—
343C22×D5—61no—
344C22×D5—61no—
345C22×D5—61no—
346C22×D5—61no—
347C22×D5C23×D311yescharacteristic
348C2×AGL(1,𝔽5)—21no—
349C2×AGL(1,𝔽5)—21no—
350C2×AGL(1,𝔽5)—21no—
351C2×AGL(1,𝔽5)—22no—
352C2×AGL(1,𝔽5)—21no—
353C2×AGL(1,𝔽5)—22no—
354C2×AGL(1,𝔽5)—22no—
355C2×AGL(1,𝔽5)—21no—
356C2×AGL(1,𝔽5)—32no—
357C2×AGL(1,𝔽5)—61no—
358C2×AGL(1,𝔽5)—61no—
359C2×AGL(1,𝔽5)—61no—
360C2×AGL(1,𝔽5)—62no—
361C2×AGL(1,𝔽5)—62no—
362C2×AGL(1,𝔽5)—61no—
363C2×AGL(1,𝔽5)—62no—
364C2×AGL(1,𝔽5)—61no—
365C2×AGL(1,𝔽5)#23912yes—
366C2×C4×C5—31no—
367C2×C4×C5—32no—
368C2×C4×C5—62no—
369C2×C4×C5C2×C4×D312yes—
370C2×C4×C5C2×C4×D311yescharacteristic
371C2×Dic5—31no—
372C2×Dic5—32no—
373C2×Dic5—62no—
374C2×Dic5C2×C4×D312yes—
375C2×Dic5C2×C4×D311yescharacteristic
376C4×D5—22no—
377C4×D5—22no—
378C4×D5—61no—
379C4×D5—62no—
380C4×D5—61no—
381C4×D5—62no—
382C4×D5—62no—
383C4×D5—62no—
384C4×D5#23712yes—
385C4×D5#23912yes—
386C23×C4—151no—
387#117—31no—
388#117—152no—
389#117—152no—
390#117—151no—
391#117—151no—
392#117—151no—
393C2×C4⋊C4—51no—
394C2×C4⋊C4—51no—
395C2×C4⋊C4—52no—
396C2×C4⋊C4—151no—
397C2×C4⋊C4—151no—
398C2×C4⋊C4—152no—
399C2×C22⋊C4—152no—
400C2×C22⋊C4—151no—
401C2×C22⋊C4—151no—
402C2×C22⋊C4—152no—
403C2×C42—51no—
404C2×C42—152no—
405C2×C42—152no—
406C2×C42—152no—
407C2×C42—151no—
408#95—52no—
409#95—151no—
410#95—152no—
411#95—152no—
412#95—151no—
413#95—152no—
414#95—152no—
415C2×C3×C5C2×#11711yescharacteristic
416C2×C3×C5C4×#4111yescharacteristic
417C2×C3×C5#52011yescharacteristic
418D15—41no—
419C3×D5#55211yescharacteristic
420C3×D5#55211yescharacteristic
421C3×D5#55511yescharacteristic
422C3×D5#55511yescharacteristic
423C5×D3—41no—
424C23×C3—51no—
425C22×D3—51no—
426C22×D3—101no—
427C22×D3—101no—
428C22×D3—101no—
429C22×D3—101no—
430C22×D3—101no—
431C22×D3—101no—
432C22×D3C22×AGL(1,𝔽5)11yescharacteristic
433C2×C3×C4—51no—
434C2×C3×C4—52no—
435C2×C3×C4—52no—
436C2×C3×C4—52no—
437C2×C3×C4—52no—
438C2×C3×C4—102no—
439C2×C3×C4—102no—
440C2×C3×C4—101no—
441C2×C3×C4—101no—
442C2×C3×C4—102no—
443C2×C3×C4—101no—
444C2×C3×C4—102no—
445C2×C3×C4—101no—
446C2×C3×C4—102no—
447C2×C3×C4—101no—
448C2×C3×C4C22×AGL(1,𝔽5)12yes—
449C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
450C2×Dic3—52no—
451C2×Dic3—51no—
452C2×Dic3—52no—
453C2×Dic3—102no—
454C2×Dic3—102no—
455C2×Dic3—101no—
456C2×Dic3—101no—
457C2×Dic3—101no—
458C2×Dic3—101no—
459C2×Dic3—101no—
460C2×Dic3—102no—
461C2×Dic3—102no—
462C2×Dic3—101no—
463C2×Dic3—102no—
464C2×Dic3—101no—
465C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
466C2×Dic3C22×AGL(1,𝔽5)12yes—
467C4×D3—22no—
468C4×D3—102no—
469C4×D3—102no—
470C4×D3—102no—
471C22×C5—61no—
472C22×C5—61no—
473C22×C5—61no—
474C22×C5C22×C4×D311yescharacteristic
475C2×D5—61no—
476C2×D5—61no—
477C2×D5—61no—
478C2×D5—121no—
479C2×D5—121no—
480C2×D5—121no—
481C2×D5—121no—
482C2×D5C2×#23711yescharacteristic
483C2×D5#100411yescharacteristic
484C2×D5C2×#23911yescharacteristic
485C2×D5C2×#23911yescharacteristic
486C2×D5D3×#4111yescharacteristic
487C2×D5#101011yescharacteristic
488AGL(1,𝔽5)—22no—
489AGL(1,𝔽5)—41no—
490AGL(1,𝔽5)—42no—
491AGL(1,𝔽5)—62no—
492AGL(1,𝔽5)—121no—
493AGL(1,𝔽5)—122no—
494C4×C5—22no—
495C4×C5—61no—
496C4×C5—62no—
497C4×C5#89212yes—
498Dic5—22no—
499Dic5—61no—
500Dic5—62no—
501Dic5#89212yes—
502C24—151no—
503C22×C4—31no—
504C22×C4—51no—
505C22×C4—51no—
506C22×C4—52no—
507C22×C4—52no—
508C22×C4—51no—
509C22×C4—151no—
510C22×C4—151no—
511C22×C4—152no—
512C22×C4—151no—
513C22×C4—151no—
514C22×C4—151no—
515C22×C4—151no—
516C22×C4—152no—
517C22×C4—302no—
518C22×C4—302no—
519C4⋊C4—31no—
520C4⋊C4—52no—
521C4⋊C4—51no—
522C4⋊C4—102no—
523C4⋊C4—152no—
524C4⋊C4—151no—
525C4⋊C4—202no—
526C4⋊C4—302no—
527C4⋊C4—602no—
528C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
529C22⋊C4—32no—
530C22⋊C4—152no—
531C22⋊C4—152no—
532C22⋊C4—152no—
533C22⋊C4—302no—
534C22⋊C4—302no—
535C22⋊C4—602no—
536C42—32no—
537C42—102no—
538C42—152no—
539C42—152no—
540C42—152no—
541C42—302no—
542C42—304no—
543C42—304no—
544C3×C5#234611yescharacteristic, complemented, Hall
545C22×C3—51no—
546C22×C3—51no—
547C22×C3—51no—
548C22×C3—51no—
549C22×C3—51no—
550C22×C3—51no—
551C22×C3C23×AGL(1,𝔽5)11yescharacteristic
552C2×D3—21no—
553C2×D3—21no—
554C2×D3—21no—
555C2×D3—101no—
556C2×D3—101no—
557C2×D3—101no—
558C2×D3—201no—
559C2×D3—201no—
560C2×D3—201no—
561C2×D3—201no—
562C3×C4—22no—
563C3×C4—52no—
564C3×C4—102no—
565C3×C4—102no—
566C3×C4—202no—
567C3×C4—201no—
568C3×C4#413012yes—
569Dic3—21no—
570Dic3—22no—
571Dic3—102no—
572Dic3—101no—
573Dic3—102no—
574Dic3—202no—
575Dic3—201no—
576C2×C5—121no—
577C2×C5C2×#89211yescharacteristic
578C2×C5#554611yescharacteristic
579C2×C5C4×#23911yescharacteristic
580D5—121no—
581D5#561611yescharacteristic
582D5#564211yescharacteristic
583D5#569411yescharacteristic
584D5#573411yescharacteristic
585C23—31no—
586C23—51no—
587C23—151no—
588C23—301no—
589C23—301no—
590C23—301no—
591C23—301no—
592C23—301no—
593C23—301no—
594C2×C4—31no—
595C2×C4—32no—
596C2×C4—51no—
597C2×C4—52no—
598C2×C4—52no—
599C2×C4—52no—
600C2×C4—52no—
601C2×C4—62no—
602C2×C4—102no—
603C2×C4—102no—
604C2×C4—101no—
605C2×C4—101no—
606C2×C4—101no—
607C2×C4—102no—
608C2×C4—101no—
609C2×C4—102no—
610C2×C4—102no—
611C2×C4—101no—
612C2×C4—152no—
613C2×C4—151no—
614C2×C4—152no—
615C2×C4—302no—
616C2×C4—302no—
617C2×C4—302no—
618C2×C4—302no—
619C2×C4—301no—
620C2×C4—301no—
621C2×C4—301no—
622C2×C4—301no—
623C2×C4—302no—
624C2×C4—301no—
625C2×C4—302no—
626C2×C4—301no—
627C2×C4—302no—
628C2×C4—302no—
629C2×C4—301no—
630C2×C4C2×D3×AGL(1,𝔽5)12yes—
631C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
632C2×C3—51no—
633C2×C3—51no—
634C2×C3—51no—
635C2×C3—51no—
636C2×C3C2×#413011yescharacteristic
637C2×C3#41×AGL(1,𝔽5)11yescharacteristic
638C2×C3#6626611yescharacteristic
639D3—41no—
640D3—201no—
641C5#7597911yescharacteristic, complemented, Sylow
642C22—51no—
643C22—51no—
644C22—51no—
645C22—51no—
646C22—51no—
647C22—51no—
648C22—61no—
649C22—61no—
650C22—61no—
651C22—301no—
652C22—301no—
653C22—301no—
654C22—601no—
655C22—601no—
656C22—601no—
657C22—601no—
658C22C22×D3×AGL(1,𝔽5)11yescharacteristic
659C4—22no—
660C4—52no—
661C4—61no—
662C4—62no—
663C4—102no—
664C4—102no—
665C4—201no—
666C4—202no—
667C4—302no—
668C4—301no—
669C4—302no—
670C4—601no—
671C4—602no—
672C4#9190712yes—
673C3#1061713311yescharacteristic, complemented, Sylow
674C2—51no—
675C2—51no—
676C2—51no—
677C2—51no—
678C2—121no—
679C2—601no—
680C2C2×#9190711yescharacteristic
681C2#1175684611yescharacteristic
682C2AGL(1,𝔽5)×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radicalC22×D3×D5C23
cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2346
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11752371C2semidirect
3. C3×#65712C2semidirect
6. #11751846C2semidirect
8. AGL(1,𝔽5)×C4⋊Dic3C2semidirect
10. #11751832C2semidirect
11. #11751751C2semidirect
25. #91781C4semidirect
26. C5×#892C4semidirect
30. #91403C4semidirect
31. #91400C4semidirect
33. #91347C4semidirect
34. #91338C4semidirect
47. #65712D3semidirect
205. #892AGL(1,𝔽5)semidirect
544. C3×C5#2346semidirect
641. C5#75979semidirect
673. C3#10617133semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D5×#8922
#117523712
C3×#657122
#117518552
C4×(C2×D3)⋊AGL(1,𝔽5)2
#117518462
#117518412
AGL(1,𝔽5)×C4⋊Dic32
#117518362
#117518322
#117517512
#106171333
#759795